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The above is not limited to subtractions, try = 1 + 1.405*2^(-48) in one cell, Excel rounds the display to 1,00000000000000000000, and = 0.9 + 225179982494413×2^(-51) in another, same display [d] above, different rounding for value and display, violates one of the elementary requirements in Goldberg (1991) [8] who states:
The CLCG provides an efficient way to calculate pseudo-random numbers. The LCG algorithm is computationally inexpensive to use. [3] The results of multiple LCG algorithms are combined through the CLCG algorithm to create pseudo-random numbers with a longer period than is achievable with the LCG method by itself.
The Mersenne Twister is a general-purpose pseudorandom number generator (PRNG) developed in 1997 by Makoto Matsumoto (松本 眞) and Takuji Nishimura (西村 拓士). [1] [2] Its name derives from the choice of a Mersenne prime as its period length.
Simulation: Drawing one pseudo-random uniform variable from the interval [0,1] can be used to simulate the tossing of a coin: If the value is less than or equal to 0.50 designate the outcome as heads, but if the value is greater than 0.50 designate the outcome as tails. This is a simulation, but not a Monte Carlo simulation.
Dice are an example of a mechanical hardware random number generator. When a cubical die is rolled, a random number from 1 to 6 is obtained. Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance.
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is exactly the Lehmer random number generator output sequence y n = ay n − 1 mod (ab − 1), reduced modulo b. Choosing a different initial value y 0 merely rotates the cycle of x' s. Complementary-multiply-with-carry generators
SP800-90 series on Random Number Generation, NIST; Random Number Generation in the GNU Scientific Library Reference Manual; Random Number Generation Routines in the NAG Numerical Library; Chris Lomont's overview of PRNGs, including a good implementation of the WELL512 algorithm; Source code to read data from a TrueRNG V2 hardware TRNG